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Conceptual Design Of Long-span Cantilever Constructed .

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Conceptual design of long-span cantileverconstructed concrete bridges(Konceptuell utformning avkonsolutbyggda betongbroar med långaspann)byJosé Diogo HonórioTRITA-BKN. Master thesis 254, Structural Design &Bridges 2007ISSN 1103-4297ISRN KTH/BKN/EX—254—SE-ihur man uppmuntrar barn att inte börja röka

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AbstractBridge design is a very delicate matter. One may argue that being a masterpiece, thebeauty of a bridge can only be seen and felt from individual to individual and notaccepted by the whole community. There was always the curiosity to know if thisassumption was true and, in that case, the reason why.There will be a brief introduction both to the cantilever method and the evolution of thismethod itself through time and a closer look and the world leading long-span bridges oftoday.As this thesis is a conceptual study of bridge design for cantilever constructed concretebridges, we aim to get good design notions, that is, the guidelines we need to follow inorder to project a pleasant looking bridge, and then evaluate this type of bridgesthroughout the world to see if what we have learned is what it is being made. And if not,the reason behind it.The second part of the thesis is more objective. Using case studies we will see thedifference, in terms of material usage and consequent cost, between bridges built with themain purpose of good design and bridges built with the main purpose of being economic.From there we will learn the consequences of our choice basing ourselves on the terms ofcomparison between the two solutions.By the end of our work, we will have developed a critical analysis towards a bridge, interms of achieved design, and also distinguish the case were we should privilegeeconomy over design, and vice-versa. With this thesis we hope we could enlighten a bitmore the subject of bridge design for cantilever constructed prestressed concrete bridges.- iii -

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PrefaceFrom the very first day I began my academic studies I had the dream to go and studyabroad. For that, I thank my home university IST and KTH for giving me thatopportunity and let me live this indescribable experience.I begin to thank my Professor and Mentor Håkan Sundquist who was always available tohelp and motivate me with great passion for the theme and work itself.I would also like to thank to my amazing group of friends both in Portugal and the new Imet during my stay in Stockholm, with a special regard to both my Tyresö friends and theHammarby Rugby team for their great family spirit.Finally a special “thank you” to my family and girlfriend for supporting me everyday.-v-

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NotationLatin charactersUnitdginfmDistance between the bottom flange and the center of gravitydgsupmDistance between the top flange and the center of gravityebottom flangemThickness of the bottom flangeetop flangemThickness of the top flangeewebmThickness of the webfcdMPaDesign compressive strength of concreteftMPaTension of the prestress tendonshmCross section height in the pier sectionlmHalf of the length of span (L/2)tmCross section height in the middle of the span sectionyimOrdinate of the center of gravity of the element iygmOrdinate of the center of gravity of the cross sectionm2Area of the bottom flangeCapital Latin charactersAbottom flange2AtmArea of the prestress tendonsAwebsm2Area of the websFprestressKNPrestressing forceIm4Moment of Inertia in relation to a neutral axisLmLength of the spanMKNmMomentMbottom flangeKNmMoment of the bottom flangeMtKgMass of prestress tendonsMwebsKNmMoment of the websPKN/mDeadweight- vii -

Ptop flangeKN/mLoad caused by the top flangePwebsKN/mLoad caused by the websVKNShear force3Vtop flangemVolume of the top flangeVbottom flangem3Volume of the bottom flangeVtm3Volume of the prestress tendonsVTOTam3Total volume of the superstructure when the ratio h/t 2.7VTOTbm3Total volume of the superstructure when the ratio h/t 4Vwebsm3Volume of the webs3WinfmFlexion module of the bottom part of the cross sectionWmaxm3Flexion module of the upper part of the cross section at the pierm3Flexion module of the upper part of the cross section in themiddle of spanWminm3Flexion module of the upper part of the cross sectionγKN/m3Volumetric weightσcMPaCompression tensionσtMPaTraction tensionm2Difference between two areasWsupGreek charactersCapital Greek charactersΔA- viii -

Contents1. Introduction .11.1. Objective .11.2. Bridge Design .11.3. Case Studies .22. Cantilever Method .33. Historical Overview .74. Aesthetics .115. Evaluation of built bridges .176. Optimum measures .316.1. Economy .316.2. Dimensioning .326.3. Quantity of Material .426.3.1. Concrete .426.3.2. Steel 486.4. Cost analysis .526.4.1. Concrete .526.4.2. Steel 526.4.3. Deck 537. Conclusion 55References .57- ix -

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1. Introduction“When the history of our time is written, posterity will know us not by a cathedral ortemple, but by a bridge”- Montgomery Shuyler, 1877, writing about John Roebling’s Brooklyn Bridge1.1. ObjectiveLong span concrete box girder bridges allowed Man to build longer and better bridges.Due to its size and importance these types of structures are sure to create an impact.Consequently, there is, or should be, an effort made in order to make the bridge not onlya structure but a piece of art as well.Throughout this work we are going to study the aesthetic guidelines for good design andbuild our case studies based on these same guidelines. Then, a conceptual study will bemade and the case studies will be evaluated and compared according to the volume ofmaterial (concrete and steel) used by each and, therefore, its final cost. By the end of ourstudies our objective is to get a notion of the values implicit when referring to design,dimensions, material and cost of the superstructure of a long span concrete box girderbridge.1.2. Bridge DesignEver since the ancient times, when it comes to large scale constructions, there is thegeneral need to make a good impact among the beholders, whether for the greatness, forits simple beauty or even both.Bridges are structures that, due to its connecting function, tend to be more isolated fromother constructions thus, creating a bigger impact. So, Humankind has always tried tofind new ways of improving the aesthetics and the design of bridges. Due to theseconstant advances, the length of the bridges started to get bigger and bigger along withthe impact that they caused. After the basic functions of the bridge were fulfilled(security and safety), there was the need to make to turn a structure into a monument, asymbol of the place where it was built. Bearing this in mind, engineers and bridgedesigners tried to cope size with beauty. With this, bridges were no longer seen as just away to connect two places, but as monument or construction which represented the city.The structural elements of the bridge were now carefully aimed to be organized in a waythat produced a pleasantly looking outcome.However, good design has a cost, a price. Sometimes the cost for a better lookingsolution doesn’t justify its improvement. Other times, the importance of the constructionitself can justify the extra amount of money.All in all a bridge with a good design surpasses the mere concept of a linkingconstruction and becomes a mark for all the years yet to come.-1-

1.3. Case StudiesOne of our objectives is to find the difference of material usage and respective cost forlong span concrete box girder bridges; therefore, we will study bridges with differentlengths of span (Figure 1 - L), ranging from 100 to 300m, and each example is spaced by50m from the next – 100, 150, 200, 250 and 300m.Our case studies will have a varying height of the cross section, as we see in Figure 1.And, as we will further see, the ratio h/t plays an important part in both bridge aestheticsand cost. So, for each span length we will study two superstructures: One with a ratio h/tof 2.7 and the other with a ratio h/t of 4.Figure 1 – Generic model of our case studiesAs for the cross section used, we know that for this type of bridges the only compatiblecross section, due to the properties that will later be listed, is the box girder – Figure 2.a)Figure 2 – Box girder section at the pier section and at mid span, respectively.However, for our project we will simplify the box girder into Figure 2.b). As this is astudy made especially for comparing solutions we know that our interest is not the finalresult of one solution alone but its comparison with another one. For that reason we choseto simplify our cross section.-2-

2. Cantilever MethodThe Cantilever Method consists in building the bridge from a supporting end, such as apier, using segments which range form 3 to 6m. This method can be executed:-Symmetrically, for each side of the pier;Asymmetrically, from one end.In the case of presstressed concrete bridges, each segment is presstressed as it is built –Figure 3Figure 3 – Scheme of the cantilever method starting from a pierBoth the deadweights of each segment and the equipment are supported by the parts ofthe structure which are already built and presstressed. The connection of the deck is thenmade trough a “closing segment” with a length from 2 to 3m. In the following figure wecan see the final stage of the cantilever method in the building of the Norwegian bridge –Raftsundet:Figure 4 – Raftsundet Bridge, NorwayThis method has the advantage of not needing any kind of structure supported in theterrain in order to hold the superstructure. Therefore it is extremely useful to build overdifficult or inaccessible terrains, such as water and incoherent soil as we will see furtheron in a brief historical overview.-3-

Due to its high cost, the cantilever method is, when possible, used with other constructionmethods:-Scaffolding towers– Figure 5;Counterweight in one end of the cantilever – Figure 6.The choice between the first and the second auxiliary methods relies on the accessibilityof the terrain below the bridge. That is, in situations such as deep valleys or traffic roadsthat cannot be obstructed.Figure 5 – Construction of a deck using the cantilever method and scaffolding towersFigure 6 – Construction of a deck using the cantilever method and a counterweight on the opposite sideThe closure of cantilevers (Figure 4) has also changed from the first solutions to the upup-to-date ones. The first bridges used a hinged positioned in the middle of span (wherethe cantilevers from each side met) – Figure 7Figure 7 – Bridge built with the cantilever Method using a central hinge-4-

The hinges allowed axial displacements and rotations. Like this, the effects caused byvariations of temperature, creep and retraction of the concrete were eliminated. However,this solution had the following inconvenient:- The need of a joint in the middle of each span;- A possible problem with the span’s articulations throughout the years.Nowadays, it is preferable to use continuous systems – Figure 8Figure 8 - Bridge built with the cantilever MethodNo only do they avoid using joints, the weak points of a bridge, but they also have a goodcapacity of stress redistribution which allows the structure to absorb the effects caused bycreep, retraction of the concrete, variations of temperature and settlement of supports.Nevertheless, when projecting a bridge of thus kind, one must bear in mind these effects.-5-

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3. Historical OverviewIt is in the Human Nature to try to reach the unreachable, to keep on pursuing moregoals and to acquire more knowledge in every field of interest.Bridge construction has been suffering many changes throughout the years, whether forthe type of material or the construction technique used. The basic function of a bridge isto serve mans need to surpass geographical obstacles, and as these obstacles kept gettingbigger, man had do find new ways of reaching the other side.The box girder section was the last solution found, for prestressed concrete bridges, tobuilt greater spans due to its characteristics:- A bottom flange which allows the cross section to be more resistant tocompression forces, thus, less deformations caused by creep actions;- Increased resistance to torsion making this cross section ideal for bridges with ahorizontal radius;- Increased slenderness and, therefore, a superstructure with less height, makingthe bridge more transparent;As a matter of fact, these properties allowed these bridges to be built using the CantileverMethod. This method is used for long span bridges and every time the terrains bellow thebridge deck are inaccessible.Historically, the Cantilever Method began to be used with wooden bridges, but becamemore commonly used with steel bridges. In 1930, in Brazil, the first concrete bridge wasbuilt using this method. The Bridge over Rio do Peixe (Figure 9), with a main span of68.5m, had to be built out of both piers, as we can see, in order to eliminate the flood riskwhich could raise the water level up to 10 m in just a few hours.Figure 9 – Bridge over Rio do Peixe, Brazil-7-

Although this was this achievement was a turning point for concrete bridge building, itwas not recognized at that time.A great pioneer of concrete bridge building and designing was Freyssinet (1879 – 1962)with the creation of prestress. Although the initial purpose of using prestress was toeliminate cracks and possible deformations through the creation of a beneficial state ofstress, the increase of load capacity gained from the use of high-strength reinforcementwas an important side effect. Among his projects one can highlight the Luzancy Bridge(Figure 10), in France, with a main span of 55 m, where simplicity and beauty is wellachieved through the use of prestressed concrete.Figure 10 – Luzancy Bridge, FranceFreysinnet considered that prestressed concreted was a completely new material andwould only accept the use of full prestressing, that is, the complete elimination of tensilestresses in the concrete, under the action of service loads. His ideas were kept for manyyears.After World War II, there was a boom in bridge construction. The first years thatfollowed the war were very important for the development of prestressed concretebridges where several new construction techniques and new design were tested andapproved. From this period, the major contributions were given by, the German, FritzLeonhardt (1909-1999) and his book - Prestressed Concrete – Design and Construction.-8-

It was in the beginning of the 1950s that the cantilever method was fully recognized to beextremely useful to prestressed concrete bridge building by, the German, UlrichFinsterwalder (1897 – 1988). His first construction was the Lahn Bridge, 1951; with aspan of 62 m, but his knowledge in this particular subject lead him to the construction ofNibelungen Bridge (Figure 11). This structure, with considerably bigger spans –101.65m, 114,2m and 104.2m – managed to capture worldwide attention and became amark for long span bridges, in prestressed concrete.Figure 11 – Nibelungen Bridge, GermanySo, for spans, the cantilever method was the only one perfectly viable. With this method,Finsterwalder, surpassed himself and built the Bendorf Bridge over the Rhine with a,remarkable, 202 m span. With this achievement he managed to prove that prestressedconcrete could compete with steel both in costs and deck height reduction.Nowadays, the longest span belongs to Shibanpe Bridge (Figure 12), built in 2005, witha main span of 330 m. However, it is the only one to use steel girder in its main span and,therefore, its achievement is not fully acknowledged by most of the structural engineers.Figure 12 – Shibanpe Bridge, China-9-

When building the Shibanpe Bridge, in order to eliminate one central pier as well asmaintaining the desired span-length while minimizing the effects caused by shear andbending, a 100 m long steel box section was placed middle of span between theprestressed concrete box girders.In spite of having a span 29 m shorter than the Shibanpe Bridge, the Stolmasundet Bridge(Figure 13) is, actually, considered to hold the present world record span for freecantilevering concrete bridge due to the fact the superstructure materials consist purely inconcrete and prestressed concrete.Figure 13 – Stolmasundet Bridge, NorwayIn the Stolma Bridge, parts of the main span were built using a mix of high strength andlightweight concrete. The design and construction were carried out on the basis of thehigh experience Norwegian have with this type of bridges. In fact, as we can see in Table1, four, out of the leading bridges in the world, are in te S.JoaoSkyeConfederationHuanghuayuanSpan301 m298 m298 m270 m260 m260 m252 m250 m250 m250 m43 x 250 m3 x 250 mLocationAustevoll, NorwayLofoten, NorwayMosjöen, NorwayGuangdong, ChinaBrisbane, AustraliaKristiansand, NorwaySichuan, ChinaSemmering, AustriaOporto, PortugalSkye Island, ScotlandNorthumberland, CanadaChongqing, 9971999Table 1 – The leading long-span prestressed concrete girder box Bridges in the World.- 10 -

4. Aesthetics“Successful design of a perfect structure can never be performed only on the basis ofgeneral rules concerning structural system, dimensions and proportions alone, as long asthe design lacks in originality and individuality.”- Christian MennIn the second half of the 20th century there was the general worldwide concept of buildingeconomical solutions. Nowadays, the concern in building esthetically pleasing bridges isgrowing again. In fact, when bridges started to be built by the ancient civilizations, suchas the Romans and the Greek, they were created in order to fulfill two purposes:Functionality and Beauty. For that reason, we still admire and look upon most of thebridges and monuments made by them.The bridge concept goes far beyond being a mere construction, it is a link between toplace, two communities. It is a way of reaching new places. It is in the human nature tobe proud of what one owns or of the place ones lives in. With bridges is not different,they cause so much impact within the society that, in the good cases, they become asymbol of that region, for the beauty they have or the status and prosperity they represent.Like the Crni Kal Viaduct (Figure 14), in Slovenia, that, besides belonging to themotorway, also serves as a stage for the well known cycling sports event – Giro d’Italia.Figure 14 – Crni Kal Viaduct, SloveniaFigure 15 – Vecchio Bridge, FranceOne can evaluate a bridge through two different aspects: as an independent identity or asan element of a larger landscape. These two can, either, cope or be independent, howeverthere can be structures that are aesthetically appealing as an independent element but donot integrate in their surroundings and vice-versa.Therefore, when dealing with a bridge project, the designer must not neglect eitheraspect, as it can be seen in Michel Placidi’s Vecchio Bridge – Figure 15. This bridge was- 11 -

completed in 1999, in Corsica. This structure is part of the highway that makes theconnection between Bastia and Ajaccio; this highway not only crosses beautiful valleysbut is also implanted in difficult terrains. The bridge has a total length of 222 m and amain span of 137.5 m. The structural combination of open truss form webs represented aworld premier.Bridge aesthetics can be evaluated in terms of harmony and efficiency. The first oneconcerns mainly the bridge integration with its surroundings, and t

As this thesis is a conceptual study of bridge design for cantilever constructed concrete bridges, we aim to get good design notions, that is, the guidelines we need to follow in order to project a pleasant looking bridge, and then evaluate this type of bridges throughout the world to see if what we have learned is what it is being made.